Random walks are well known from probability theory. I have the idea for hash walks. If h(x) is a hash function and a,b,c,d,e,f is a boolean sequence then the sort of hash walk I am talking about is h(x+a), h(h(x+a)+b), h(h(h(x+a)+b)+c),....
At each step in the hash walk there are only two possible next states. If the input data is sparse then you will frequently have walks that are the same. I use the idea to construct prediction trees. At the moment I am working on the idea of using Bloom filters to greatly reduce the amount of memory needed to store hash walks.
In information theory terms could you get even better generalization using less than 1 bit of input per walk step? Is there any prior literature on this topic?